Radical ExpressionsSimplification, Rationalization and Operations

What are radicals? A radical is an expression that expresses

the square roots, cube roots etc. The following are examples of radicals:

, , , , , , , ,

Simplifying Radicals We say that a square root radical is

simplified, or in its simplest form, when the radicand (the number inside) has no square factors.

The following are examples of radicals in simplest form: , 2,

The following are examples of radicals in simplest form: , 3, 2

How do we simplify radicals? STEP 1: Find the prime factors of the radicand.

Try these:

How do we simplify radicals? STEP 1: Find the prime factors of the radicand.

Try these:

1. = 2. = 3. = 4. =

5. = 6. = 7. = 8. =

How do we simplify radicals? STEP 2: For each pair of same prime factor, send

it outside the radical.

Try these:

How do we simplify radicals? STEP 2: For each pair of same prime factor, send

it outside the radical.

Try these:

1. = 2. = 3. =

4. = 5. = 6. = 7. =